Hi Andreas,

thanks a lot. I think the crucial point really is to note that the threshold estimation is always conditional on a threshold being present in the first place. Maybe I can extend the printed output a little in a future version to make this clearer.

So when I run your application with the heterosked. switch set to on/TRUE, then everything makes sense: The test result says "LM-test for no threshold: 7.864104 / Bootstrap p-value: 0.778000", so no threshold is found. Hence the following threshold estimation should probably be ignored.

Numerically, the new (90%) CI under heteroskedasticity is then [0.505766, 0.597225]. Looking at the sorted version of your threshold variable "test_var", the relevant portion is: 

2000:05     0.505766
2004:06     0.515507
2015:01     0.528682
2011:08     0.597225

So the algorithm says that at the 90% level the threshold would be among one of those four realizations in the sample. Previously, (under the false assumption of homoskedasticity) the CI was completely focused on the one realization 0.528682. I readily admit that it's a little counter-intuitive that with a non-existing / non-identified threshold the notional CI is very tight instead of very loose, but then we need to remember that the estimate puts the threshold at a pretty extreme value into the trimming range of the test. (As before, with only 3% of the observations in the 2nd regime here.)

@Note to self: The plot "F Test For Threshold" has a strange scaling of the x-axis. It seems to fit the lhs variable d_EA_nfc_td better than the threshold (and x-axis label) variable test_var. (This problem does not appear with the sample script.)

Bottom line: Fortunately I cannot see any substantial problem with the package here, it's almost all about the funny data that you have which imply a lot of clear heteroskedasticity.

cheers

sven

Dear Sven,

Thank you for the suggestions. I attach the data and a minimal program to replicate the results. Any feedback or change in the code is welcome.

Best regards,

Andreas

On Tuesday, April 8, 2025 at 07:02:22 PM GMT+2, Andreas Zervas <anzervas@yahoo.com> wrote:

Many thanks,

Most likely a small sample problem (the estimate from the first function leaves 18% of observations in first regime, while that of the second even less). However, maybe you should decide what is the preferred approach to estimate the threshold, so that results do not differ.

Many thanks though for the program and the reply.

Best regards,

Andreas

P.S.

The commands I use are (no other parameter is pre-set):

bundle b_nfc_td_@vn = H_thresh_test(d_EA_nfc_td, l1, test_var, FALSE, 1000, 0.95, 0.15)

b_nfc_td_@vn = H_thresh_estim(d_EA_nfc_td, l1, test_var, FALSE, 0.9, 0.7, 2)

and the output is:

Test of Null of No Threshold Against Alternative of Threshold
Under Maintained Assumption of Homoskedastic Errors

Number of Bootstrap Replications: 1000
Trimming percentage: 0.150000

Threshold Estimate: 0.160979
 (18 % of obs in 1st regime)
LM-test for no threshold: 25.684802
Bootstrap p-value: 0.009000

*******************************************
Threshold regression based on Hansen (2000)
User choice: assume homoskedasticity
*******************************************
Global OLS Estimation, Without Threshold

Dependent Variable: d_EA_nfc_td
OLS Standard Errors Reported

             coefficient   std. error     z      p-value
  -------------------------------------------------------
  Constant   -0.00673135   0.00420391   -1.601   0.1093  
  d_DFR       0.483153     0.0314844    15.35    3.78e-53 ***
  d_DFR_1     0.303526     0.0317247     9.567   1.10e-21 ***
  d_DFR_2     0.166300     0.0316151     5.260   1.44e-07 ***
  d_DFR_3    -0.0447660    0.0312387    -1.433   0.1518  
  d_DFR_4    -0.0825148    0.0310742    -2.655   0.0079   ***

  Observations = 301
  Degrees of Freedom = 295
  Sum of Squared Errors = 1.56605
  Residual Variance = 0.00530865
  R-squared = 0.692068
  Heterosked. test p-val = 0.000971344

*************************************************************
Threshold Estimation, dependent variable: d_EA_nfc_td

Threshold Variable: test_var
Threshold Estimate = 0.528682    90% CI: [0.528682, 0.528682]
Sum of Sq. Errors = 1.18205    Residual Var. = 0.00409013
Joint R-squared = 0.768
Heterosked. test p-value: 0.000

*************************************************************
Regime 1: test_var <= 0.528682
 (standard errors do not take into account threshold uncertainty)

             coefficient   std. error      z      p-value
  --------------------------------------------------------
  Constant   -0.00301783   0.00374876   -0.8050   0.4208  
  d_DFR       0.434563     0.0285556    15.22     2.68e-52 ***
  d_DFR_1     0.329858     0.0284484    11.59     4.37e-31 ***
  d_DFR_2     0.173306     0.0281670     6.153    7.61e-10 ***
  d_DFR_3    -0.0265575    0.0281749    -0.9426   0.3459  
  d_DFR_4    -0.0782675    0.0283734    -2.758    0.0058   ***

  Observations = 292
  Degrees of Freedom = 286
  Sum of Squared Errors = 1.14915
  Residual Variance = 0.00401801
  R-squared = 0.74057

Regime 2: test_var > 0.528682
 (standard errors do not take into account threshold uncertainty)

             coefficient   std. error     z      p-value
  -------------------------------------------------------
  Constant    -0.138555    0.0277248    -4.998   5.81e-07 ***
  d_DFR        1.20773     0.142826      8.456   2.77e-17 ***
  d_DFR_1     -0.306680    0.156734     -1.957   0.0504   *
  d_DFR_2      0.443741    0.237662      1.867   0.0619   *
  d_DFR_3     -0.275100    0.169861     -1.620   0.1053  
  d_DFR_4      0.284360    0.123145      2.309   0.0209   **

  Observations = 9
  Degrees of Freedom = 3
  Sum of Squared Errors = 0.0328959
  Residual Variance = 0.0109653
  R-squared = 0.934906

 

On Tuesday, April 8, 2025 at 04:49:22 PM GMT+2, Andreas Zervas <anzervas@yahoo.com> wrote:

Hi all, especially Sven,

I was playing with the package thres_infer, and it appears that the threshold estimates from functions H_thresh_test() and H_thresh_estim() differ. Is it intented? Should they be the same? In the particular example from the sample script, which I pasted below, the values are similar, but I run it with data that give totally different results.

Any thought - suggestions?

Best regards,

Andreas

gretl version 2024d
Current session: 2025-04-08 16:37

# Sample script for thresh_infer

Read datafile C:\Program Files\gretl\data\misc\denmark.gdt
periodicity: 4, maxobs: 55
observations range: 1974:1 to 1987:3

Listing 5 variables:
  0) const    1) LRM      2) LRY      3) IBO      4) IDE    

Test of Null of No Threshold Against Alternative of Threshold
Under Maintained Assumption of Homoskedastic Errors

Number of Bootstrap Replications: 1000
Trimming percentage: 0.150000

Threshold Estimate: 0.088000
 (46 % of obs in 1st regime)
LM-test for no threshold: 4.154898
Bootstrap p-value: 0.923000

*******************************************
Threshold regression based on Hansen (2000)
User choice: assume homoskedasticity
*******************************************
Global OLS Estimation, Without Threshold

Dependent Variable: mg
OLS Standard Errors Reported

             coefficient   std. error      z      p-value
  -------------------------------------------------------
  Constant    0.0705718    0.0272334     2.591    0.0096  ***
  IBO        -0.469693     0.229408     -2.047    0.0406  **
  IDE         0.110332     0.500081      0.2206   0.8254

  Observations = 54
  Degrees of Freedom = 51
  Sum of Squared Errors = 0.0487311
  Residual Variance = 0.000955512
  R-squared = 0.162774
  Heterosked. test p-val = 0.365732

*************************************************************
Threshold Estimation, dependent variable: mg

Threshold Variable: IDE
Threshold Estimate = 0.074    90% CI: [0.074, 0.11]
Sum of Sq. Errors = 0.0435625    Residual Var. = 0.000907553
Joint R-squared = 0.252
Heterosked. test p-value: 0.225

*************************************************************
Regime 1: IDE <= 0.074000
 (standard errors do not take into account threshold uncertainty)

             coefficient   std. error      z      p-value
  -------------------------------------------------------
  Constant    -0.833454     0.386015    -2.159    0.0308  **
  IBO         -0.774593     0.915857    -0.8458   0.3977
  IDE         13.4116       6.06844      2.210    0.0271  **

  Observations = 5
  Degrees of Freedom = 2
  Sum of Squared Errors = 0.00612267
  Residual Variance = 0.00306133
  R-squared = 0.425631

Regime 2: IDE > 0.074000
 (standard errors do not take into account threshold uncertainty)

             coefficient   std. error      z      p-value
  -------------------------------------------------------
  Constant    0.0727286    0.0303053     2.400    0.0164  **
  IBO        -0.487763     0.233237     -2.091    0.0365  **
  IDE         0.116314     0.505722      0.2300   0.8181

  Observations = 49
  Degrees of Freedom = 46
  Sum of Squared Errors = 0.0374399
  Residual Variance = 0.000813911
  R-squared = 0.178561

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